Restrictions on Iran, as well as on Venezuela, come amid already tight supply as the OPEC has been withholding output this year.
Brent crude oil futures were at $69.94 per barrel, 6 cents, or 0.1 percent, above their last close.
On U.S. -China trade front, accusing China of backtracking on commitments in trade talks, the U.S. has threatened to further increase U.S. trade tariffs on Chinese goods.
Iran's eight biggest oil buyers - China, India, Japan, South Korea, Italy, Greece, Turkey and Taiwan - had received the USA waivers last November, which had allowed them to continue importing limited volumes of Iranian crude.
The U.S. dollar rose and the Chinese offshore yuan stayed hobbled near 2-1/2 month lows on Tuesday after U.S. President Donald Trump's threat of additional tariffs on Chinese goods rattled traders, though both moves were modest. The dollar index rose 0.01 per cent, with the euro unchanged at US$1.12.
China's crude oil imports in April unexpectedly surged to a record despite refinery maintenance outages and tepid domestic fuel demand, customs data showed, as state-run refiners built up stocks of Iranian crude oil anticipating a sanctions clampdown.
U.S. West Texas Intermediate and international-benchmark Brent crude oil futures are trading mixed with a slight bias to the downside on Wednesday.
On Tuesday, EIA cut its 2019 world oil demand growth forecast by 20,000 barrels per day (bpd) to 1.38 million bpd.
Most analysts expect Iran's exports to fall to a little more than 500,000 bpd from about 1 million bpd in April. The country is the world's biggest oil importer.
Before that, prices rallied as Washington tightened USA sanctions on Iran with the aim of reducing its oil exports to zero.
The sources said based on the rights envisioned in JCPOA's paragraph of 26 on the European Union commitments and also in paragraphs of 36 and 37 which are about dispute resolution mechanism, Iran plans to decrease some of its commitments and resume a number of its nuclear activities that have been ceased under the JCPOA.